Show that when X is a binomial random variable. [Hint: First express E(X) as a sum with lower limit

. Then factor out np, let so that the sum is from to , and show that the sum equals 1.] y 5 0 y 5 n 2 1 x 5 1 y 5 x 2 1 E(X) 5 np

(n 2 x)

B(x; n, 1 2 p) 5 1 2 B(n 2 x 2 1; n, p)

b(x; n, 1 2 p) 5 b(n 2 x; n, p)

V(X) 5 0 p (0 # p # 1)

X 5 the number